Divide the following complex numbers: $\dfrac{10(\cos(\frac{4}{3}\pi) + i \sin(\frac{4}{3}\pi))}{2}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $10(\cos(\frac{4}{3}\pi) + i \sin(\frac{4}{3}\pi))$ ) has angle $\frac{4}{3}\pi$ and radius 10. The second number ( $2$ ) has angle $0\pi$ and radius 2. The radius of the result will be $\frac{10}{2}$ , which is 5. The angle of the result is $\frac{4}{3}\pi - 0\pi = \frac{4}{3}\pi$ The radius of the result is $5$ and the angle of the result is $\frac{4}{3}\pi$.